Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+8y &= -8 \\ -4x+y &= -5\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {4x-5}$ Substitute this expression for $y$ in the first equation. $4x+8({4x - 5}) = -8$ $4x + 32x - 40 = -8$ Simplify by combining terms, then solve for $x$ $36x - 40 = -8$ $36x = 32$ $x = \dfrac{8}{9}$ Substitute $\dfrac{8}{9}$ for $x$ back into the top equation. $4( \dfrac{8}{9})+8y = -8$ $\dfrac{32}{9}+8y = -8$ $8y = -\dfrac{104}{9}$ $y = -\dfrac{13}{9}$ The solution is $\enspace x = \dfrac{8}{9}, \enspace y = -\dfrac{13}{9}$.